Li/Li+, respectively. Lastly, to lay out the principles for rational design of quinone-based cathode materials beyond the current work, we constructed and discussed the quantitative structure property relationships of quinones based on the data generated from the calculations.Organic cathode materials are attractive candidates for the development of high-performance Li-ion batteries (LIBs). The chemical space of candidate molecules is too vast to be explored solely by experiments; however, it can be systematically explored by a high-throughput computational search that incorporates a spectrum of screening techniques. Here, we present a time- and resource-efficient computational scheme that incorporates machine learning and semi-empirical quantum mechanical methods to study the chemical space of approximately 200 000 quinone-based molecules for use as cathode materials in LIBs. By performing an automated search on a commercial vendor database, computing battery-relevant properties such as redox potential, gravimetric charge capacity, gravimetric energy density, and synthetic complexity score, and evaluating the structural integrity upon the lithiation process, a total of 349 molecules were identified as potentially high-performing cathode materials for LIBs. The chemical space of the screened candidates was visualized using dimensionality reduction methods with the aim of further downselecting the best candidates for experimental validation. One such directly purchasable candidate, 1,4,9,10-anthracenetetraone, was analyzed through cyclic voltammetry experiments. The measured redox potentials of the two lithiation steps,  The search for quinone-based lithium-ion battery cathode materials within a vast chemical space. Among the variety of organic motifs, conjugated carbonyls are one of the earliest investigated energy storage materials for battery applications, whose history dates back to the 1970s.6 To date, carbonyl-containing organics, such as quinones,7 aromatic imides,8 anhydrides,9 and ketones,10 have been explored as electrode materials for LIBs.Redox-active organic materials, including carbonyls,7,11 However, in comparison to state-of-the-art inorganic cathode materials, small quinones have not yet been found to be sufficiently viable in terms of actual redox potentials and cycling stability.12–14 Improvements in the electrochemical performance of quinone-based cathode materials are possible by fine-tuning their molecular structure through different approaches, including functionalization with R-groups,15 fusing aromatic16 or heteroaromatic rings17 together, and incorporation of additional redox-active carbonyl groups.18Quinone-based small molecules are particularly attractive in the research community as they offer high theoretical specific capacity and promising redox stability and can be sourced from biomass.19–24 However, previous computational studies on quinone-based LIB cathode materials have been restricted to a modest number of molecules which were derived from a limited range of often intuitively chosen quinone core structures, including cyclohexa-2,5-diene-1,4-dione (BQ),25–27 naphthalene-1,4-dione (NQ),25,28,29 anthracene-9,10-dione (AQ),29–34 and phenanthrene-9,10-dione (PQ).17,29,34 These investigations of chemical spaces, although around few quinone core structures, have offered useful insights on the effectiveness of various strategies, such as functionalization and ring-fusion. However, the effect of these strategies, especially in terms of often competing performance requirements, has not yet been sufficiently well explored for a large range of quinones that span across several functional groups, ring numbers and the number of redox-active carbonyl groups that can interact with Li.Going beyond the Edisonian experimental approach of trial-and-error, high-throughput computational screening (HTCS) has emerged as a powerful approach for accelerating the discovery of high-performing material candidates. Owing to the ever-increasing computational power and the new analysis tools that are based on robust theoretical approaches, HTCS has become an efficient means for the exploration of large ‘virtual chemical spaces’.In this work, we tapped into a large chemical space of systematically enumerated quinones by means of HTCS with two principal goals: (1) finding the top-performing candidates which can be validated experimentally and (2) deciphering the trends in battery performance-related properties induced by pondered molecular engineering. The structure-property relationships emerging from the second step can be used as guiding design principles for future discovery efforts. The workflow of chemical space exploration of organic molecules conceptualized and applied in this work is shown in Library generation: a virtual library consisting of 199 498 unique quinone molecules was designed and developed by employing three elementary molecular building-blocks and four chemically different R-groups.• Property computations: an automated search for the commercial availability of the virtual library molecules in the ZINC database35 was performed, in which matching records for a total of 245 compounds were found. In addition, the simplified molecular input line entry system (SMILES) representations of all the virtual library molecules were used as inputs for a machine learning (ML) model that predicts the synthetic complexity score (SCScore) of the molecules. Next, we employed semi-empirical quantum mechanics (SEQM) calculations to optimize the geometries of molecules and to calculate their redox potentials via a linear regression model. Furthermore, the theoretical gravimetric charge capacity (Q) and energy density (W) of the virtual molecules were calculated.• DFT simulations: a small proportion of the entire library of 199 498 molecules, which were either commercially available or easily synthesizable, was treated with density functional theory (DFT) calculations. Accordingly, 641 molecules were further optimized and their properties were recalculated at a higher level of accuracy. In addition, to determine the stability of molecules, we used a structural alignment algorithm and analyzed the deviations between DFT-optimized structures of the pre- and post-lithiated molecules.• Virtual screening: out of the 641 candidates that have been considered in DFT-calculations, 430 molecules have satisfied the molecular stability criterion enforced in the current work. Moreover, 349 of these 430 molecules have met the prescribed criterion for redox potential. Lastly, we employed the Uniform Manifold Approximation and Projection (UMAP) dimension reduction technique in combination with the tailored similarity method in order to obtain a non-linear dimensional reduction of the top-candidate molecular chemical space.• Experimental validation: for real-lab validation, we performed electrochemical measurements on a readily purchasable molecule from the list of top-compounds that had been identified via the virtual screening.• In addition to providing a list of top-grade quinone-based candidate molecules for LIBs, we also included here a structure–property analysis of the entire virtual library molecules.2.2.1.para position), 1,2-benzoquinone (carbonyl groups at the ortho position) and benzene. The usage of 1,4- and 1,2-benzoquinones as building blocks for the core structures theoretically promotes a 2e−–2Li+ reaction, thus enabling ring aromatization during the lithiation process.12 The building blocks were then fused to exhaustively generate all possible CQSs that had a maximum of four six-membered rings. This constraint was implemented based on the expectation that the single-molecule approximation for prediction of cathode properties will likely become more erroneous with increasing number of rings due to increasing π-stacking interactions.36 PBM data was replaced with SVG by xgml2pxml:<glyph-data id="z.dbd" format="PBM" resolution="300" x-size="8" y-size="10" xml:space="preserve">00000000000000000000000000000000111111110000000011111111000000000000000000000000</glyph-data><svg xmlns="http://www.w3.org/2000/svg" version="1.0" width="13.200000pt" height="16.000000pt" viewBox="0 0 13.200000 16.000000" preserveAspectRatio="xMidYMid meet"><metadata>Created by potrace 1.16, written by Peter Selinger 2001-2019</metadata><g transform="translate scale" fill="currentColor" stroke="none"><path d="M0 440 l0 -40 320 0 320 0 0 40 0 40 -320 0 -320 0 0 -40z M0 280 l0 -40 320 0 320 0 0 40 0 40 -320 0 -320 0 0 -40z"/></g></svg>O groups; in other words, a maximum of two quinone building block molecules per CQS were allowed. Applying these two structural constraints, 170 unique CQSs were generated, which can be classified into five main groups based on the number and position of carbonyl groups. The molecules that consist of one 1,4-benzoquinone ([P]), one 1,2-benzoquinone ([O]), two 1,4-benzoquinone ([P + P]), two 1,2-benzoquinone ([O + O]), and one 1,4-benzoquinone and one 1,2-benzoquinone ([P + O]), are shown in In addition to the size constraint, the CQSs contained either two or four CR-groups: –Cl, –CH3, –OCH3, and –NH2. These electron-withdrawing and electron-donating chemical groups were chosen to enlarge the electrochemical window of the CQSs.13,37,38 Each CQS was exhaustively enumerated using a single type of R-group without combining different R-groups. The range of functionalized positions of R-groups varied between zero and the maximum number of H atoms that are present on that specific CQS. The enumeration of the virtual library was performed automatically using the Custom R-Group Enumeration tool as implemented in Schrödinger Materials Science Suite (SMSS).39 An overview of the statistical decomposition of the virtual library, which contained 199 498 unique quinone-based molecules, is shown in R-group functionalized derivatives per CQS, are given in ESI Table S1.†Finally, the CQSs were functionalized by replacing the peripheral H atoms on the rings with four different 35 This tool uses SMILES strings of molecules as inputs and collects the available vendor information from the ZINC database. The search resulted in matching records for 245 organic compounds, which represents a tiny fraction (0.13%) of the grand virtual library that has been built in the current work. This indicates a vast chemical space of molecules that can possibly be synthesized and explored for application as quinone-based cathode materials in LIBs.After generating the virtual library, an automated search for finding the commercially available (CA) molecules was performed using an in-house developed tool on the ZINC database, which contains vendor information data on 750 million purchasable compounds.2.2.et al.,40 which provides an assessment of not directly the synthesizability but the synthetic complexity of organic molecules. The model to assign the SCScore was developed by training an artificial neural network on nearly 12 million known chemical reactions. It accepts the SMILES string of a molecule as the input and returns its predicted SCScore on a continuous scale from 1 to 5, where a high SCScore indicates high complexity  of precedent synthetic routes for a compound, and vice versa.While HTCS studies report numerous promising new compounds, their synthesizability is a crucial aspect that is often overlooked during screening. This is partly due to the lack of reliable and rigorous descriptors of synthesizability of organic compounds. In an attempt to address this crucial aspect, we calculated the SCScore, a recently proposed metric by Coley 2.3.41 force field using the MacroModel42 module in SMSS. Next, geometry optimization (OPT) and single-point-energy (SPE) calculations were performed for the whole library at the SEQM-level with the AM1 method default parameters.43 For these SEQM calculations, the MOPAC2016  energies of the quinone reactant molecules that have been optimized at the AM1-level as a descriptor for predicting the redox potentials of all the molecules in the virtual library. Accordingly, the applied linear regression equation is given as: and  denote the predicted redox potential and LUMO energy of quinone-based molecules computed at the SEQM-level, respectively. For a group of 641 down-selected candidates, further OPT and SPE calculations were performed at a higher DFT-level of accuracy using the B3LYP functional46,47 with the LACVP++**48 basis set with diffuse and polarization functions. The DFT calculations were performed using the Jaguar program49 as implemented in SMSS. The change in energy and RMS density matrix were separately converged to within 5.0 × 10−5 and 5.0 × 10−6 Hartree, respectively. A ‘medium’ grid density was chosen for performing OPT, whereas a ‘fine’ grid density was used for SPE calculations. Similar to the above, the DFT-calculated LUMO energy of the optimized quinone reactant molecule was employed to predict redox potential. Meanwhile, it has been reported that the electronic structure, particularly the average electric potential of carbon atoms in carbonyl-equipped rings, demonstrates a linear correlation with the redox potential of quinone molecules.17 Here, we compared the prediction performance of the two chemical descriptors, and the fitting results are shown in Fig. S1.R2 = 0.97) shows better prediction performance than the average electric potential of carbon atoms in carbonyl-equipped rings (R2 = 0.81). Similarly, the linear regression equation is given as: and  denote the predicted redox potential and LUMO energy of quinone-based molecules computed at the DFT-level, respectively. It should be noted that both 6 with a (w/w = 1 : 1) solution mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC).50The redox potentials of quinone-based molecules were predicted at the SEQM-level of theory for the entire virtual library and at the DFT-level for a select group of 641 molecules. At first, the lowest-energy conformers of all the molecules in the gas phase were pre-optimized with the OPLS3e016 ref.  software2.4.Q, which represents the number of charge carriers per unit mass of active cathode material. While the real value of Q for any cathode material will depend on its actual structural composition, molecular packing, and thus determined density, a theoretical upper limit of Q can be defined as:51M is the molecular weight of the quinone molecules in g mol−1, n is the number of transferred e−, and F is the Faraday constant. For quinone-based molecules in the current work, we assumed that n is equal to the number of carbonyl groups in a CQS. The molecular weights were calculated using the SMILES as inputs in SMSS. Similarly, the W of organic cathode materials is defined as:51E° represents the average redox potential of the cathode material with respect to Li/Li+. The molecular dataset containing the calculated Q and W values has been provided in the ESIAnother primary metric of electrochemical performance of cathodes is their 2.5.27,30 but also as redox active materials in flow batteries.24,26,52 The mechanisms that cause chemical instability in quinones differ not only depending on their molecular structure but also on the electrochemical environment of the surrounding electrolyte, the charge–discharge potentials and rates, and impurities. For use as electrode materials, the change in internal bond lengths upon (de)lithiation is one of the important descriptors of chemical stability because significant bond changes in redox-active molecules are likely to result in instability due to geometrical and mechanical deformations of the electrode.24,53–57 Apart from these, structural deformation upon electron transfer is strongly correlated to the molecule's reorganization energy,26 which affects the (de)lithiation kinetics.The chemical stability of quinones is a widely debated topic, not only because of their use as electrode materials58 which is an iterative and heuristic tool for atom-level structural comparisons of the molecules. We used the DFT-level optimized reactant and product molecular geometries for the comparisons. To ensure consistency over the explored space of candidate molecules, the calculation of RMSD was based only on the carbon backbones of the pre- and post-lithiated CQSs.65 The backbone carbon atoms were selected not only because they represent proportionally the largest atomic fraction count in quinone backbones but also because they undergo significant aromatization-driven changes due to lithiation. It must be noted that the inclusion of the contribution of non-core atoms to RMSD is anyway likely to be erroneous in the gas phase approximation that has been adopted here. This is because the reorganization of these peripheral atoms are highly likely to be affected by the inter-molecular interactions in the solid phase.In the current study, to scrutinize the structural changes upon lithiation, we calculated the root mean square deviation (RMSD) between the reactant and product molecules for all the down-selected 641 candidates. For this task, we employed the LS-align algorithm,2.6.59 to effectively visualize the final screened set of 349 molecules for further analysis and selection of the best candidates for experimental validation. ChemPlot includes three types of dimensionality reduction methods to convert high-dimensional data into visually interpretable two-dimensional plots. A motivation here for applying the dimensionality reduction methods was to find molecules for experimental validation that are structurally ‘different’ from molecules that have previously been investigated in the literature. To start with, we classified the molecules in the set of 349 as either already-investigated, CA or low-SCScore. We used the UMAP60 and tailored-similarity methods, both as implemented in ChemPlot, for visual clustering of the 349 molecules.We used ChemPlot26,27 NQ,29 AQ,29–34 PQ,17,29,34 and several others18,61,62 found in our screening library, have been investigated in recent literature as cathode materials for LIBs. Thus, these molecules were classified as already-investigated. After excluding the already-investigated molecules from the screened dataset of 349 molecules, the rest of the molecules that were commercially-available were classified as CA otherwise as low-SCScore. To utilize ChemPlot, we fed it a two-column dataset comprising the SMILES representation of molecules in the first column and their corresponding three categorical target values  in the second column. ChemPlot's tailored similarity approach works by initially computing all available descriptors for each molecule, which are then collated into a matrix format, with the rows representing the individual molecules and the columns representing their respective descriptors. The software then identifies which calculated descriptors are correlated with the categorical target values. Finally, the resulting matrix of selected descriptors is utilized as an input for the dimensionality reduction phase.It is important to note that some CQSs, such as BQ,2.7.−1, Sigma-Aldrich) with a mass ratio of 8 : 1 : 1. In particular, the organic active material was ground with super P in an agate mortar for 15 minutes to obtain the black mixed powder, which was subsequently dispersed in N-methylpyrrolidone  solution with the dissolved PVDF (0.05 g ml−1). The mixed slurry was treated by ultrasonication for 30 minutes and cast on Al foil. The half-cell consisted of a working electrode, lithium metal , and a glass fiber separator , while the cell assembly was performed in an argon-filled glove box. The electrolyte is composed of a solution mixture of EC and DMC (v/v = 1 : 1) with 1.0 M LiPF6 . The cyclic voltammetry (CV) measurements were conducted using a galvanostat/potentiostat  with a scan rate of 0.2 mV s−1.The electrodes for the electrochemical measurements were fabricated by mixing the active material 1,4,9,10-anthracenetetraone (AT) with super P and polyvinylidene difluoride  = 2.2, 95% of the CA molecules had an SCScore < μ. In addition, the SCScore distribution of molecules is observed to be positively biased towards the molecules that accommodate a small number of R-groups. This is expected since the synthesis of molecules that contain a large number of functional groups will be more complex. All these observations support both the aptness of the SCScore as a first-order metric for describing the synthesizability of the virtual molecules and the screening of these molecules on the basis of their SCScores.The scatter plot of the predicted SCScores and  values of 2.5 ± 0.2 V vs. Li/Li+. On a more detailed inspection, it is found that a majority (∼81%) of the CA molecules were the functionalized derivatives of only four different quinones, namely, BQ , NQ , AQ , and PQ . In previous experiments, the  values of NQ and AQ were between 2.3 and 2.5 V vs. Li/Li+, whereas PQ had .29,50,61 Next, molecules that have both a low-SCScore (≤2.2) and small number of functional groups (≤4) were down-selected for further screening. This resulted in 396 low-SCScore molecules from the library that were not CA. These molecules had 1.90 <  < 4.25 (±0.03) vs. Li/Li+, which is a wider potential window than has previously been exercised with quinone-based materials at LIB cathodes.45 Given the large variety of functional groups available in the chemical literature, we surmise that the synthesis of quinones with targeted redox potentials is unlikely to be a bottleneck.The predicted redox potentials of the CA molecules were found to be in the lower range, as shown in 45 In order to proceed further with higher accuracy, DFT calculations have been performed to recalculate the redox potentials of the 641 molecules. As a side note, the parity plot comparing SEQM (AM1) data against DFT (B3LYP) data is shown in R2) of 0.12 V vs. Li/Li+ and 0.94, respectively, imply that the AM1 method is sufficiently accurate when used for the purpose of the initial ranking of molecules in a large virtual library.Next, we grouped together 245 CA and 396 low-SCScore molecules, thus reaching a total of 641 molecules, for further screening. It has previously been shown that DFT is more accurate than SEQM when predicting the redox potentials of quinones, with the normalized root-mean-square errors (NRMSE) being 12.65% and 16.10%, respectively.. We found no clear correlations between the calculated RMSD values and either of  or chemical functional group type. Nevertheless, it is observed that the molecules functionalized with –Cl groups tend to have higher RMSD , thus making them more likely to undergo degradation. Drawing any inferences on the stability of candidate molecules based on RMSD analysis needs validation against experimentally backed metrics. However, such analysis is currently not possible due to the lack of such corroborating experimental data in the literature. Still, we recommend candidates with low RMSD values for experimental validation. Theoretically, the lengths of single, aromatic, and double bonds between the two neighboring carbon atoms in a molecule are 1.54, 1.40, and 1.33 Å, respectively.63 Thus, as a crude approximation, we posit a maximum tolerable value of change in the bond length for an aromatic bond as 0.14 Å (i.e. single-aromatic) because bond length changes larger than 0.14 Å will likely be more prone to structural deformation and degradation. Subsequently, applying this criterion to the group of 641 molecules, which is demarcated by the horizontal line in To evaluate the 641 molecules based on their structural stability and reaction kinetics, we calculated the RMSD of backbone carbon positions between the DFT-optimized structures of pre- and post-lithiated molecules. 29–34 The calculated  and  values for AQ were 2.30 and 2.28 V vs. Li/Li+, respectively, which are both consistent with the experimentally reported value of 2.27 V.50,61 Targeting molecules with a redox potential higher than AQ, 349 of 430 molecules were found to have  ≥ 2.28 V vs. Li/Li+, as demarcated by the vertical line in Continuing the down-selection process, we considered the predicted redox potential values as a metric. The most extensively investigated quinone, both in experiments and computations, is AQ.Finally, to determine the molecules for experimentation in the current study, we visualized the clustering of the 349 quinones by using ChemPlot . The pri and Q of the 349 molecules. As can be observed in  and Q regions. Interestingly, many of the already-investigated molecules were located in proximity to the CA molecules. Consequently, these molecules were not prioritized for experimental validation in the current study, as our main interest is in molecules that have not been studied for LIB cathodes.The , Q, and W. Thus, we prioritized molecules #2, #3 and #4 for experimentation and among them we selected molecule #4 (AT) for electrochemical characterization based on its in-stock commercial availability.As the prime candidates for our experiments, we focused on the CA molecules that were located in the same clusters as a large number of low-SCScore molecules. Accordingly, five CA quinones were identified in three different clusters of low SCScore virtual molecules that are pointed out using the black arrows in 3.2.via HTCS as explained above. We performed CV analysis of the candidate compound in a half cell against lithium metal. The open circuit voltage of the half-cell containing the initial electrode with a pristine active organic material was measured to be approximately 2.6 V, which indicates its promising nature as an electrode for LIBs. As shown in vs. Li/Li+, as shown with vertical dotted lines in  and the B3LYP  methods  on molecules shifts the predicted redox distribution towards higher potentials  and J. Z. ; writing – review and editing, X. Z., A. K., M. H., R. A. J. J. and S. E.; supervision, A. K., R. A. J. J. and S. E.; project administration, S. E.; funding acquisition, X. Z. and S. E. All authors have read and agreed to the published version of the manuscript.There are no conflicts to declare.DD-002-D2DD00112H-s001DD-002-D2DD00112H-s002


Highly efficientcoupling of light from an optical fiberto siliconnitride (SiN) photonic integrated circuits (PICs) is experimentallydemonstrated with simple and fabrication-tolerant grating couplers(GC). Fully etched amorphous silicon gratings are formed on top offoundry-produced SiN PICs in a back-end-of-the-line (BEOL) process,which is compatible with 248 nm deep UV lithography. Metallic backreflectors are introduced to enhance the coupling efficiency (CE)from −1.11 to −0.44 dB in simulation and from −2.2to −1.4 dB in experiments for the TE polarization in the C-band.Furthermore, these gratings can be optimized to couple both TE andTM polarizations with a CE below −3 dB and polarization-dependentlosses under 1 dB over a wavelength range of 40 nm in the O-band.This elegant approach offers a simple solution for the realizationof compact and, at the same time, highly efficient coupling schemesin SiN PICs. Silicon nitride photonicshas gained attention in the past decades due to numerous advantages,such as propagation losses below 0.1 dB/m, dispersion engineering,negligible two-photon absorption, wide transparency window, low thermalsensitivity, and low sensitivity to fabrication variations.8 EC on SiN further benefits from the low index contrastof the waveguides, making it easier to match the modal size betweenon-chip waveguides and the optical fiber, with CEs reaching below1 dB.11 GC, on the other hand, allows out-of-plane couplingand therefore wafer-level testing, eliminating the need for intensiveprocessing of a sensitive optical facet at the edges of the chipswhile typically exhibiting relaxed fiber alignment tolerances.8 The main drawbacks of GC compared to EC, however,are the lower bandwidth, lower coupling efficiency, and high polarizationdependency. SiN grating couplers have an improved bandwidth in comparisonto silicon ones due to the lower index contrast,12 allowing 1 dB bandwidths of up to 80 nm.13 The second challenge of low CE, however, is further hamperedon SiN, as lower index contrast results in a lower scattering strength,yielding CEs of −4.2 dB in single-etch SiN gratings.12 To address this, different approaches have beenproposed and demonstrated. Most commonly, multilayer distributed Braggreflectors17 consisting of silicon layers beneath the SiN waveguide are employed,yielding CEs as low as −1.17 dB in measurement and −0.31dB in simulation with a 40 nm 1 dB bandwidth.14 A different approach consists of defining grating bars on multiplelayers,21 requiring precise planarizationand lithographical alignment. Experimental results show CE of −1.29dB and a high 1 dB bandwidth of 80 nm13 and simulations of −0.39 dB.21 A simpler dual-layer GC is demonstrated with a SiN grown on SOIyielding −2.5 dB CE in the C-band,19 although deep trenches through a triple-layer consisting of SiN,SiO2, and Si must be etched. Utilizing the self-imagingmethod, −1.5 dB CE has been achieved with a staircase gratingand a fiber placement over 100 μm above the surface.22 Overcoming the third challenge of polarizationdependency is vital for applications, such as on–off keyingreceivers in optical communications, where polarization of the incominglight is not known a priori.23 Solutionsare more difficult, however, as matching of the Bragg condition fortwo polarizations at the same time is hindered by the typical birefringenceof planar waveguides. Possible solutions include 2D grating couplersdemonstrated on silicon,25 that typically splitthe polarizations into two different directions. For 1D grating couplers,only a few examples exist, such as combining two grating periods withan experimental CE of −7.8 dB and a polarization dependentloss (PDL) of 0.8 dB over 20 nm26 or amultilayer grating consisting of two SiN and one silicon layer witha demonstrated CE of −4.8 dB and 1dB PDL of over 100 nm.18 Despite the impressive grating coupler demonstrations,a method that includes fabrication tolerance and simplicity suitedfor rapid prototyping, while also achieving low loss in the C- andO-bands and polarization insensitivity, is still missing on SiN.To couple lightefficiently to the SiN platform, two state-of-the-artmethods exist: edge coupling (EC) and grating coupling (GC). EC, onthe one hand, is typically known for its high performance in termsof CE, bandwidth, and polarization insensitivity.In this work, we introduce a simple and fabrication tolerant methodto couple light efficiently into foundry-produced SiN waveguides withsilicon overlay gratings; see 28The work in this paper is in partbased on ourresults first publishedat the Optica APC congress in 2021 and 2022.The grating coupler presented in this workconsists of amorphoussilicon (a-Si) grating bars on top of an 800 nm thick SiN layer separatedby a thin interlayer oxide (ILO) between the a-Si and the SiN, see 0 mode is propagated from left to right in the SiN waveguide.A sketch of the mode profile is given in 1, TE2, TE3) of the multimode section;see Conceptionally, one can understandthe couplingscheme from ky = 2π·sin(θ)·ncladding/λ is the wave vector componentin y-direction, i.e., the out-of-plane wave, β= 2π·nGC/λ is the propagationconstant of the multimode waveguide and |K| = 2π/Λthe grating vector. Assuming a diffraction angle θ toward thenormal axis, the phase-matching equation can be rewritten tonGC is the effective index of the waveguide grating section, ncladding is the refractive index of the cladding,θ is the diffraction angle, λ the center wavelength, andΛ the pitch of the grating.8In the next step, we can derive an approximatevalue for the pitchΛ of the grating. Toward this end, we follow the general designprinciples of a 1D grating coupler. To diffract the incoming lightinto a fiber, the phase matching condition or Bragg condition, whichrelates the wave vectors of the incident beam and the diffracted beams,must be fulfilled. This can be expressed asnGC by averaging the effective index of the etchedand unetched region weighted by the fill factor (FF):nM is the effective index in the unetched region, nE is the effective index in the etched region, and FF= LM/(LM + LE) is the fill factor. To apply this approximationto a multimode structure, see nM of the unetched part in the grating waveguide can be approximatedby a weighted average of the effective indices of the respective modes.18 The relative weights are given as the fractionsby which each mode is excited.This equation can be solved for Λ if the effective indexof the multimode grating section were known. Here, we approximate hSi using the weighted average method with an FF of 0.32. We find anearly constant value despite a large variation in hSi. This shows a large tolerance of the grating couplertoward a variation of hSi. Following,we investigate the origin of this fabrication tolerance. Toward thisgoal, we plot in 1, TE2, and TE3 from 0, see hSi, we find that the effective indexof the unetched region nM to be near constantfor a large range of hSi values. Thisis an interesting finding as nM is theweighted average of the modes. Next we investigate the variation of nM with the interlayer-oxide thickness (hILO). 2 and (d)of TE3 in relation to hSi.The colors indicate hILO. It can be seenthat hILO has little influence on theeffective index of the two modes. This leads to the conclusion thatthis a-Si overlay grating coupler has a high tolerance on both hSi and hILO.hSi = 290 nm, hILO = 100 nm with a pitch of Λ = 888 nmand fill factor of FF = 0.32. The thicknesses of the SiN (hSiN = 800 nm) and buried oxide (hBOX = 4.1 μm) are kept constant during the optimization.In thissection, we show the simulation results of the C-band grating couplerfor a maximum CE of −0.42 dB. We analyze the fabrication parametersto show the large fabrication tolerance of our approach. The phase-matchingcondition allows us to pick a reasonable starting condition for thegrating around which we can apply a thorough 2D FDTD analysis. Theoptimization routine has led us to an optimized grating coupler withparameter values of The wavelength tolerance of the coupling efficiencies of the SiNwaveguide toward a SMF fiber tilted by an angle of 7° is shownin Indeed, it is found that the CE can be furtherincreased to −0.44dB by adding a metallic back reflector below the buried oxide (4.1μm below the SiN); see hSi, hILO, Λ, FF, hBOX, andthe thickness of the top oxide (hTOX).In each sweep, we kept the other parameters constant. In hSi. Each color indicates a different hILO. In (b), we plot the coupling efficiency as a function of hILO. Each color indicates a different hSi. The individual simulations are indicatedby colored dots. We find a 1-dB tolerance of 86 nm for hSi and 139 nm for hILO, indicatingan exceptional large tolerance over the two parameters. In LM by as much as 129nm. Finally, hBOX (redline) and hTOX (yellow line). Varying hBOX results in an oscillating behavior arisingfrom constructive and destructive interference of the reflectionsat the interface of the buried oxide and the silicon handle wafer.From the yellow curve, it is seen that hTOX behaves similarly, and a maximum CE is observed at 1.25 μm.Typically, there is a trade-off between efficiency and bandwidth.30 If higher optical bandwidth is required, one could potentially utilizean overlay grating material with a lower refractive index than siliconat the price of lower coupling efficiency.In a next step, we analyze the fabrication tolerance of our idealgrating coupler without metal mirror; see 31 Furthermore, the dual-polarization capability of integratedcomponents is essential for the realization of polarization multiplexingschemes or the compensation of polarization rotating effects in thesystem.In the nextstep, we design and demonstrate a dual-polarization (or polarizationinsensitive) 1D grating coupler for the O-band using the same principleas the O-band coupler described in the previous section. The use ofO-band wavelengths has become the standard for intradatacenter interconnectsdue to the zero-dispersion window around 1310 nm.1, TE2, TE3, and TE4 and (b)TM1, TM2, TM3, and TM4 is shown in relation to hSi. Similarto the C-band, the weighted average is almost constant. With the additionof TE0 and TM0, the effective indices in thegrating region can be designed to be nearly equal for TE and TM polarization. This yields a similar pitch through the approximationof the phase matching equation. To achieve similar behavior in theC-band, control over hBOX and hSiN is necessary, which are fixed by the foundryin our work. We used the weighted average approximation describedin the TE,dB – CETM,dB|, is below 0.15 dB over a wavelength range of 30 nm. The gratinghas a pitch of Λ = 765 nm and a fill factor of 0.484. The thicknessof the a-Si is 305 nm and of the interlayer oxide 100 nm.We overcome the polarization sensitivity of 1D gratingcouplers, which arises due to the birefringence of rectangular waveguides,by taking advantage of the large fabrication tolerances to exploitand the degree of freedoms provided by the overlay structure to finda low loss grating coupler for the TE as well as the TM modes. Incontrast to the C-band grating coupler, there are not three but fourmodes in the multilayer structure because of the smaller wavelength.In 2 with a comparable refractive index (n ≈ 1.48). We fabricated the dual-polarization grating couplerin the same way as the C-band gratings with hSi = 305 nm and without a back reflector. The SEM image ofthe O-band grating coupler is found in Thea-Si overlay grating coupler was fabricatedwith a back-end-of-the-line process on a foundry-produced thick SiNplatform. Amorphous silicon was deposited on a planarized sample withplasma-enhanced chemical vapor deposition, patterned with electronbeam lithography, and etched by using inductively coupled reactiveion etching (ICP-RIE) in HBr plasma. The fabrication of the deviceswith metallic reflector included a backside oxide etch with ICP-RIEand a subsequent deep reactive ion etching (DRIE) of the Si substrate.Electron beam evaporation was used to deposit gold on the backside. hBOX due to over etching.The plots in Inthis work, we introduce highly efficientgrating couplers foran emerging SiN platform. The single etch a-Si gratings have beenfabricated by a back-end-of-the-line process at the wafer-scale onfoundry-produced SiN waveguides. For TE-polarized light in the C-band,simulations yield high CEs of −1.11 without and −0.44dB with metallic mirrors. In experiments, we found CEs of −2.2and −1.4 dB, respectively. Furthermore, we demonstrate efficientand polarization-insensitive 1D grating couplers in the O-band. Wemeasure a PDL below 1 dB within a 40 nm spectral window with a CEof −2.3 dB (TM) and −3.0 dB (TE) in the same devicefor coupling to a fiber aligned along the same fiber angle. Our approachoffers a solution to a pending problem and provides ease of fabricationby taking advantage of a fabrication-tolerant design that is compatiblewith wafer-scale testing. The low fabrication complexity might helpto further leverage the SiN platform.


Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for time-dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids—particularly with large fractions of Fock exchange—are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections. We assess most recent TD-DFT methods on excimers and highlight shortcomings of current strategies to treat dispersion in excited states. In an excimer or exciplex, the electronically excited species causes two interacting orbitals to be singly occupied resulting in stabilisation through formation of the complex.5 This electronic stabilisation effect is short-lived, as relaxation to the ground state occurs quickly, causing repulsive intermolecular forces to oppose the relatively weak attractive forces. Energy decomposition analysis of the excimer/exciplex stabilisation energy revealed the following contributing components: electrostatics, Pauli repulsion, CT, exciton coupling and London dispersion.8,9The excited-state properties of the dimeric species are unique from those of either monomer.10 Since then, excimers have also been revealed to be crucial species in contemporary applications of technological and biological relevance. Contrary to their notoriety as an undesired energy trap for singlet-fission,11 some studies have shown potential advantages in organic electronics, such as excimer states mediating intramolecular electron transfer12 and charge separation13 or broadening the emission for white organic light emitting diodes;14 see ref. 16,17 molecular rulers,18,19 and industrial-scale lasers.20 Excimers also occur in biological systems, playing a role in the photo-damage of DNA as they can occur between nucleobases such as adenine21 and guanine.22Aromatic excimers were discovered experimentally in the fluorescence spectrum of pyrene in cyclohexane solution by a broad, structureless emission band that occurred at a lower energy than the associated monomer emission.23,24 (DFT) approaches, also called density functional approximations (DFAs), are frequently used in applications of technological relevance, including the description of exciplexes and excimers. In order to have predictive character, DFAs must be robust; i.e., they must yield results with equal accuracy or error margins across a variety of different chemical problems. Comprehensive benchmark studies have identified such generally applicable DFT approaches for ground-state problems including for thermochemistry, kinetics, and geometries, to name a few examples.25–31 In all studies, it was evident that the accurate treatment of noncovalent interactions (NCIs), in both inter- and intramolecular cases, is crucial to achieve the desired accuracy and robustness of a method. In the context of DFT, it is particularly important to properly address the correct treatment of London dispersion effects. It has been known since the mid-1990s that conventional DFAs do not capture those effects correctly.32–35 This sparked the development of various dispersion-corrected DFT techniques, some of which later turned out to be less effective than initially claimed,36–38 and others having now become the recommended default for ground-state DFT applications.39,40 We refer interested readers to recently published reviews41,42 directed at users that are unfamiliar with the field of dispersion-corrected DFT applications for ground-state problems as well as reviews that recommend the current best practice in the field,43–45 which includes dispersion-corrected double-hybrid46,47 DFAs (DHDFAs) when feasible.Computational chemistry techniques, particularly Kohn-Sham Density Functional Theory48–50 (TD-DFT) has become the method of choice to treat excited-state problems. Recent advances51–53 and detailed benchmark studies54–64 on single-molecule cases have shed light on the quality of TD-DFAs for the calculation of excitation energies. As recently summarised for readers unfamiliar with the field, lower rungs on the Jacob's Ladder of DFT65 should be avoided due to the emergence of artificial ghost states and large red shifts in excitation energies.66 Global-hybrid DFAs can be suitable for local valence excitations, subject to having the right amount of nonlocal Fock exchange (FE)—about 40%  technique72–75 applied to the exchange part of DFAs solves the long-range problem, local valence excitations tend to be blue-shifted.52,58,62,66,76 Time-dependent DHDFAs77 depend additionally on a nonlocal, perturbative electron-correlation component78 that compensates for many of the systematic errors of hybrids.47,51,54,55,57,58,66,79 In fact, our group recently developed RS-DHDFAs52,53 that belong to some of the currently most robust TD-DFT methods for a variety of different local and long-range valence excitations in organic molecules.52,53,62–64 A slightly different group of RS-DHDFAs have also proven to be very promising when used within the Tamm–Dancoff Approximation80 (TDA-DFT).81–83The binding of excimers and exciplexes inherently relies on the system's excited-state properties and is dominated by NCIs, which introduces additional complexity compared to the ground-state case. Linear-response time-dependent DFT within the adiabatic approximation40% ref.  and 66—b5 The study was unique in the sense that a London dispersion correction was rigorously applied to an excited-state study, namely the DFT-D2 ] or in its Becke–Johnson-damping97–99 [DFT-D3(BJ)40] form.100–106 To our knowledge, only three studies have considered adjusting dispersion corrections for excited states. In the first, Ikabata and Nakai107 calculated excited-state dispersion coefficients within the local-response dispersion108,109 (LRD) model to explore the interaction energies of exciton-localised molecular complexes from the S66  model for excited states of conjugated hydrocarbons, pull–pull chromophores, and CT complexes.113 While these studies considered suitable model systems, only a limited selection of DFAs were applied. These three studies, among others,114,115 would allow the conclusion that state-specific dispersion corrections for excited states should be developed, but further characterisation of current methods is necessary to provide guidance towards such future developments. The present paper intends to provide such characterisation.Compared to single-molecule cases, there are fewer systematic studies that explore NCIs in excited states of molecular complexes. However, it is expected that TD-DFT methods inherit the problems of the underlying ground-state DFA, such as the inability to properly describe London dispersion interactions. Additionally, the TD-DFT formalism itself carries problems that may further complicate the treatment of excited-state NCIs. In 2008, Huenerbein and Grimme presented a study of excimers and one exciplex across a very limited number of TD-DFAs.-D2 ref.  correctiS66 ref.  benchmar85,86,90,91,102,105,106,116 used range-separated hybrids. Of the two studies that investigated DHDFAs94,102 both utilised TDA-DFT, instead of the full TD-DFT scheme, but only Krueger and Blanquart102 considered a dispersion correction. Interestingly, most of the methods previously used to study exciplex systems are not those recommended by some of the latest single-molecule excitation studies,52,53,57,62,64,66 which by itself is reason enough to investigate the latter in the exciplex/excimer context. The majority of excimer and exciplex studies investigated these methods via applications,22,86,88,91–94,100,101,104,116 or carried out benchmark analyses against reference values that were not well defined and mostly based on experiment.5,90 Both benchmarks and application-based excimer studies focussed on comparison of methods by the calculation of the dissociation energy, as this explores the binding of the complex, while fewer studies have explored other spectrometric parameters such as the fluorescence, absorption and repulsion energies.7,85,86,104,107,116–121 Potential energy curves of the lowest excited state reported relative to the asymptote of the dissociation curve of the ground state5 are standard practice to derive these spectroscopic parameters. Ground-state studies commonly explore NCIs by focusing entirely on interaction energies that can be calculated, e.g., as the difference between the dimer and individual monomer energies or alternatively as the difference between the total energies of the dimer and a system in which the two monomers have been dissociated to a large distance from one another. By this definition, a negative interaction energy indicates a stable complex. The dissociation energy of an excimer is inherently an interaction energy and provides a convenient metric to discuss excited-state binding and NCIs in one go. However, the computational studies of excimers and exciplexes do not report excited-state interaction energy curves, other than a handful of exceptions we are aware of;7,8,85,102 we advocate to adopt them more frequently, as it allows direct comparison with what has become the standard in ground-state treatments of NCIs. Note that according to that definition of an interaction energy, the dissociation energy De is simply its absolute value.Most of the aforementioned exciplex studies used older global-hybrid DFAs, while some27,43,51,52,66 To the best of our knowledge, similar studies are missing to systematically study NCIs in excited states. In this work, we intend to initiate the first step towards more systematic studies of excited-state NCIs by restudying excimer model systems under incorporation of the latest state-of-the art TD-DFT methods. The four model systems discussed herein are the benzene, naphthalene, anthracene and pyrene dimers  levels based on truncated basis sets and at the complete-basis-set (CBS) limit in Section 3. The purpose of this analysis is to identify a suitable level of theory that can serve as a reliable, yet fast benchmark for the subsequent discussion of TD-DFT methods in various subsections of Section 4. The latter is split into different aspects: the impact of non-local FE, the behaviour of dispersion-uncorrected TD-DFT methods, the impact of using ground-state based corrections of the DFT-D3(BJ)40,96 and DFT-D4  atomic-orbital (AO) basis set and a geometry convergence criterion of 10−7 Eh. Use of the RICC2 module in TURBOMOLE limits the symmetry consideration to Abelian point groups such that all excimers are calculated with D2h symmetry. The excited-state optimised structures were used to generate non-relaxed dissociation curves as follows: the internal coordinates of each monomer were frozen, then total energies of the lowest-lying singlet excited states were calculated across a range of inter-monomer separations up to 16 Å, and then each energy was taken relative to 16 Å, which represents the asymptote for the given state. The geometry optimised excimer structures were not comprised of perfectly planar monomers, which has been previously noted during both TD-DFT and CC2 132 level have been shown to give good estimates of the equilibrium inter-monomer distance, with excimer dissociation energies that are generally overestimated by ca. 2 kcal mol−1 in the case of the benzene excimer.133 As this study uses the same structures throughout, internal comparison of the dissociation energies is reasonably justified.TURBOMOLE 7.3 ref.  was usedCC2 ref. ) level wCC2 ref.  optimisag. S1 ESI. De, is De corresponds to the dissociation energy of an excimer and therefore the terms interaction and dissociation energy are used interchangeably. Equilibrium inter-monomer distances re, corresponding to the distance at which the minimum energy arises, are also discussed in parts of our discussion.Herein, the figures display interaction energy curves such that a negative interaction energy indicates a stable dimer. In the context of this paper, 134 (RI) approximations were employed with appropriate auxiliary basis sets.135 Coupled cluster singles doubles with perturbative triples excitation correction136 [CCSDR(3)] calculations for select points along the dissociation curves were carried out with Dalton2016,137 also utilising the frozen-core approximation. The WFT calculations were used to identify suitable reference data for the subsequent assessment of TD-DFT methods.TURBOMOLE was also used for all SCS-CC2 and CC2 single-point calculations along the dissociation curves. The frozen-core and resolution of the identity138- and BLYP139–141-based methods with varying amounts of non-local exchange. However, as lower-rung DFAs have shown to be unreliable for excited-state problems,55,66 we limit our final benchmarking study to global hybrids, range-separated hybrids, global double hybrids and range-separated double hybrids; the exact functional types are detailed in 78 [CIS(D)] correction as initially suggested by Grimme and Neese;77 see ref. Single-point, linear-response TD-DFT calculations within the adiabatic approximation were conducted for all dissociation curves for a series of DFAs as listed in −7 Eh (TURBOMOLE) and 10−8 Eh (ORCA). The frozen-core approximation was applied across all TURBOMOLE calculations, and in ORCA147,148 calculations it was used along with the RI approximation for the perturbative parts of the global double hybrids. Large quadrature-grid options “7” (TURBOMOLE) and “grid6 finalgrid7” (ORCA) were used to ensure smooth dissociation curves. Dispersion corrections of the type DFT-D3(BJ)40,96 and DFT-D4  these are ref. Self-consistent-field (SCF) steps in this work were carried out with energy convergence criteria of 10-D4 ref.  and 123 A series of different basis sets—ranging from double-ζ (DZ) to quadruple-ζ (QZ)—were employed throughout this work, with some of them used for extrapolations to the CBS limit. More information is provided in the following sections.3154,155 For ground states, coupled-cluster singles-and-doubles with perturbative triples, CCSD(T),156 at the CBS limit is the ideal that many aim to achieve in contemporary benchmarking.27,157,158 It constitutes a very accurate approximation to the true interaction energy of noncovalently bound complexes in their electronic ground state.27,158–160 One excited-state equivalent to ground-state treatments with CCSD(T) is linear-response CCSD enhanced with a different type of perturbative triples correction than the aforementioned CCSDR(3).136 It delivers excitation energies that are similar to the more costly linear-response approximate coupled cluster singles doubles triples (CC3);161 for examples of CCSDR(3) and CC3 being established as benchmarks and comparisons between both, see ref. 166,167 the excited-state equivalent remains prohibitively expensive.155 For most of our systems, CCSDR(3) is therefore not achievable for computational reasons, and in the following we identify if instead CC2 or its spin-component-scaled128 variant, SCS-CC2, can be used as a low-cost alternative.Prior to analysing the performance of TD-DFT methods, a sufficiently reliable reference method that is still feasible for larger systems must be identified. An appropriate reference method should minimise the computational cost while maintaining reasonable comparability to a higher level of theory. Coupled-cluster WFT methods are considered the gold standard of chemical accuracy.51,66 That being said, as interaction energies in the excited state have not been studied frequently, little is known about the effects of truncated basis sets on interaction energies in excited states.Establishing a reference method also requires the careful choice of an appropriate basis set. Large basis sets quickly become computationally prohibitive, especially for large systems, while small basis sets are rife with errors due to being incomplete. Studies on obtaining vertical excitation energies, including studies on DHDFAs, have shown that large TZ basis sets are often sufficient to obtain nearly converged results, with little change when using QZ basis sets.168 Small basis sets also suffer from basis set incompleteness error (BSIE) which can artificially destabilise complexes through a failure to correctly describe intermolecular electron density.168 In the case of interaction energies, BSIE is not consistent with varied inter-monomer separation and will therefore not be cancelled by similar error of infinitely separated monomers in the calculation of interaction energies.169 If use of a larger basis set is not suitable, additive corrections have been developed for ground states to minimise the BSSE.170–172 BSIE corrections173,174 have also been developed although they are generally scarce and more computationally demanding. To our knowledge BSSE corrections have not yet been developed for excited states, and basis set convergence studies for such systems are sparse.121,169 Some previous exciplex studies7,8,88,90,102,104,120,121,169 opted to utilise the counterpoise correction175 to account for BSSE in exciplex binding. Our own basis set study below utilises BSSE-uncorrected interaction energies in interest of time and avoiding corrections that have not been thoroughly assessed specifically for excited states. In that way we are also able to provide a picture of current methodology that can be easily applied by method users. Moreover, we strive to use large basis sets for CBS extrapolations, which further reduces the impact of BSSE. That being said, it is worthwhile to explore the influence of counterpoise or similar corrections in later studies. A BSIE correction for excited states was recently developed Loos and co-workers that was shown to recover chemically accurate vertical excitation energies of small organic molecules with augmented double-ζ basis sets, with the exception of diffuse excited states.176 This suggests that work to establish basis set error corrections for excited states is underway, however, current methods do not seem to be robust enough yet to provide reliable corrections for our present study.The basis set superposition error (BSSE), for example, plagues the treatment of ground-state NCIs with small AO basis sets in both WFT and DFT methods. This well-known error is caused by the limited number of AOs available on a molecular fragment ‘borrowing’ the basis functions from other fragments, which artificially stabilises the multi-fragment system—such as a dimer—relative to its separate fragments.Note that we explore the CBS limit with extrapolation techniques that were originally developed for ground-state problems and have to our knowledge never been assessed for NCI energies in excited states.3.166,177 benchmark studies suggest that the latter does not show consistent improvement to vertical excitation energies in general.177,178 However, enhanced excited-state geometries and vibrational frequencies could lead to more accurate 0–0 transition energies for π → π* and n → π* excitations.179–181 Therefore, any potential improvements for SCS-CC2 seem to be problem specific, hence we need to carry out a comparison with CC2.For this section, non-relaxed dissociation curves for the first excited state of the benzene dimer were generated with CC2 and SCS-CC2 and various AO basis sets. While CC2 and SCS-CC2 both yield reliable excitation energies, albeit still above the related chemical-accuracy threshold of 0.1 eV,130,182 and Dunning [(aug-)cc-pVnZ]183,184 basis sets; where n corresponds to ‘S/D’, ‘T’, ‘Q’, respectively. All dissociation curves are shown in †To decide between CC2 and SCS-CC2, we conduct a study across DZ-, TZ-, and QZ-quality basis sets both with and without additional diffuse functions. This comparison involves both Ahlrichs [def2-nZVP(D)]r of 3.00 Å (a point in proximity of the expected minimum for this level of theory) is −11.96 kcal mol−1 (Table S2−1 (re = 2.99 Å) and −20.19 kcal mol−1 (re = 2.90 Å), respectively. While the differences between CC2 and SCS-CC2 are quite striking, the general trends show parallels to ground-state studies, where it has been established that conventional MP2 overestimates interaction energies in dispersion-driven complexes, while SCS-MP2 provides a more balanced description.28,128 CC2 has also been shown to overestimate the dispersion contribution in the same excimer complexes as studied here90 and it appears, by its closer proximity to CCSDR(3), that SCS-CC2 reduces this overestimation. Despite SCS-CC2 being in closer proximity to CCSDR(3), both CC2 variants across all basis sets explored overstabilise the excimer relative to CCSDR(3)/def2-TZVP. When inspecting −1 (def2-SVP) to −13.29 kcal mol−1 (def2-QZVP) for SCS-CC2, and from −18.22 (def2-SVP) to −20.64 kcal mol−1 (def2-QZVP) for CC2  data could not be obtained with diffuse functions. However, this decision will not influence our subsequent TD-DFT benchmark study, as long as the same type of basis set is used therein. Our final findings and conclusions are therefore unlikely to be affected by this decision.Basis sets including diffuse functions—aug-cc-pVTZ and def2-TZVPD—produce minima that are considerably lower than basis sets without diffuse functions, meaning that the absolute interaction energies are larger for both CC2 variants in those cases. As CC2 more greatly overestimates the interaction energy minima, additional diffuse functions give well depths furthest from the CCSDR(3) reference. Interestingly, def2-TZVPD produces a deeper minimum than aug-cc-pVTZ. For SCS-CC2, def2-TZVPD and aug-cc-pVTZ differ by 0.58 kcal mol Table S1. The cho−1 deeper than for cc-pVTZ. Given that Ahlrichs basis sets are computationally more efficient due to relying on fewer primitive Gaussian-type orbitals, they are our preference in this study, particularly when considering the larger dimers. In order to further clarify the best choice of basis set for SCS-CC2 as a wave function reference, CBS values are generated for CCSDR(3) and SCS-CC2 in the following section.Based on the herein discussed findings, we rule out using the CC2 method in the remainder of the study due to its greater tendency to overestimate the well depths relative to CCSDR(3). Interaction-energy curves for Ahlrichs and Dunning basis sets without diffuse functions, show reasonable agreement for SCS-CC2, with the def2-TZVP wellbeing only by 0.19 kcal mol3.2169 are strongly encouraged but such characterisation falls outside the scope of this study.The total energy calculated by a given method is expected to converge to a finite value with an increase in AO basis set size. This also leads to converging interaction energies, as indicated by the series of interaction energies ranging from DZ to QZ basis sets discussed in the previous section, with changes between TZ and QZ being smaller than between DZ and TZ. CBS extrapolations take advantage of this convergence behaviour to estimate the fully converged energy for a given family of basis sets. While the practice of CBS extrapolation is well established for ground-state studies, CBS extrapolations are scarcely conducted for excited-state problems due to a lack of established extrapolation methods. Prior to the development of established excited-state extrapolation methods, application of ground-state extrapolations should at least improve the ground state at the base of excited-state energies. This improvement of the ground-state energy is expected to extrapolate the convergence behaviour enough to give us further insight into the best comparison of SCS-CC2 to CCSDR(3). We therefore chose to employ the same extrapolation formulae and the same extrapolation exponents as in ground-state studies. Further studies to comprehensively investigate basis set convergence behaviour of NCIs in excited states, such as that conducted by Krueger and Blanquart for exciplex systems,ECCS) were obtained by adding the CCS excitation energy to the HF ground-state total energy. Such excited-state total energies for two truncated basis sets were then used to obtain the resulting CBS-limit energy with the familiar formula:186X and Y are the successive cardinal numbers of the two basis sets used, and α is a constant specific to the family of basis set used. We adopted the value of α for ground-state Ahlrichs-basis set extrapolations, namely α = 10.39 for DZ-TZ and α = 7.88 for TZ-QZ extrapolations.187In ground-state extrapolations the HF and correlation energies are extrapolated separately due to their different convergence behaviours. The equivalent to ground-state HF energy in excited-state coupled-cluster treatments is the CCS total energy as it does not include electron correlation. We conducted linear-response calculations, so CCS total energies (EC was obtained from the differences between CCS and SCS-CC2 or CCSDR(3) total excited-state energies. Those contributions were extrapolated to the CBS limit with the familiar formula for the correlation energy (EC):188β has values of 2.40 (DZ-TZ) or 2.97 (TZ-QZ), respectively.187The electron-correlation contribution ECCS(CBS) and EC(CBS) were added together to obtain the excited-state total energies. These were then used to calculate the interaction energies at the CBS level. Ideally, the basis sets used in such extrapolations should be as large as technically possible. For CCSDR(3), only DZ and TZ calculations were feasible for the benzene dimer, while TZ and QZ calculations were possible for SCS-CC2. The resulting CCSDR(3)/CBS interaction energies for the same four select intermolecular distances discussed for CCSDR(3)/def2-TZVP in the previous section are shown in −1 (r = 2.90 Å) to 0.1 kcal mol−1 (r = 3.00 Å). Both levels of theories agree for r = 3.05 Å with ΔE = −13.42 kcal mol−1. The agreement between both levels is therefore better near the minimum region of CCSDR(3)/CBS, which lies close to 3 Å /CBS interaction energy at r = 3.00 Å. In contrast, the SCS-CC2/def2-QZVP minimum is only 0.23 kcal mol−1 higher. Considering that the CCSDR(3)/CBS interaction energy at r = 3.00 Å is −13.52 kcal mol−1, the percentage errors for the SCS-CC2/TZ, QZ and CBS minima are only 2.5, 1.7 and 0.96%, respectively; see  Table S1. The SCSDe and re from minima across these basis set treatments, while the corresponding dissociation curves are given as Fig. S2–S5.re appears already close to convergence across all systems and De differs within 0.11 to 1.52 kcal mol−1.When choosing a reliable benchmark level of theory for the subsequent TD-DFT study, the accuracy of a method must be considered alongside the time and resources needed to treat the system sizes involved in this study as well as the large number of points needed to generate smooth dissociation curves. As SCS-CC2/def2-QZVP calculations are feasible across all excimer systems, obtaining SCS-CC2/CBS curves offers the potential for a reference at a standard comparable with ground-state studies. Ideally, to establish the accuracy of using this level of theory, we would want to obtain CCSDR(3)/def2-TZVP data for the larger excimer systems to offer a comparison. However, at this stage, our computational resources prevent this proposed extension. Given the low percentage errors for the benzene test case for truncated basis sets, discussed above, we obtain SCS-CC2 values for all excimers with TZ, QZ and CBS. Our main incentive for the TD-DFT benchmark is to assess the performance of modern TD-DFT methods, with and without applied dispersion corrections, based on their resulting dissociation energy curves. For this purpose, we choose SCS-CC2/CBS as the reference level for the subsequent study. We would like to point out that the curves discussed herein are an improvement on what has been acceptable in the field as binding energies with basis sets of QZ quality or higher being rare for aromatic exciplexes. Nevertheless, we recommend a future study dedicated solely to (single-reference) WFT methods that addresses CBS extrapolations and BSSE corrections more in detail. As such studies are beyond the scope of this work, we continue with the discussion of the TD-DFT results.45,90,116,120,121,133,189 While the other excimers have received some attention, they are typically studied individually92,93,104,118,119 rather than comparatively.7,8,90 The binding of an excimer involves a change in the geometry upon excitation with the eclipsed dimer, also called the “perfect sandwich” structure,3,190 widely accepted as the most stable conformation of an excimer.7,8,88,133,190 The excitation responsible for excimer formation causes a displaced ground-state dimer to move into this eclipsed form, which is also associated with a reduction in distance between the monomers.3,5 The most energetically stable intermolecular separation as determined experimentally for aromatic excimers is reported in the range of 3.0–3.6 Å.4 Our SCS-CC2/CBS re values, reported in re.7Having established SCS-CC2/CBS as a reference method for the four excimer models, it is now possible to move on to benchmarking various DFAs. Of the four excimers , benzene8 For example, parallel stacking and short intermolecular distance increases orbital overlap, promoting exciton delocalisation.102 The interplay of these various interactions may present a challenge for DFT methods to properly describe the dissociation energies and inter-molecular distances. The main focus of this section is to investigate DFAs with this in mind. Before we discuss each model system individually, we study the impact of the amount of FE on the TD-DFT dissociation energies. Each model system is then first discussed without the addition of dispersion corrections before the impact of said corrections is studied separately. This section ends with an overarching discussion across all four dimers by means of statistical analysis.The close and parallel stacking of the eclipsed formation facilitates excimer binding interactions: electrostatics, Pauli-repulsion, CT, exciton coupling and London dispersion.4.1re) between the two monomers and the stability of the dimers represented by the dissociation energy (De). The ability of each method to describe these parameters is assessed by quantitative comparison to those calculated with our SCS-CC2/CBS reference by use of signed percentage error:i represents either De or re. In this definition of percentage error, positive values represent overestimation while negative ones represent underestimation of the quantity. De (top panel) and re (bottom panel). The numerical values and corresponding dissociation energy curves are given in Section S1.4 in the ESI.†In this section, we analyse the influence of FE on the description of excimer binding by global hybrids. This analysis was performed by varying percentages of FE, between 0 and 75%, for two underlying exchange-correlation (XC) approximations, PBE and BLYP. The resulting functionals of varied FE are detailed in De and re are considerably large across all systems regardless of FE percentage. Almost all functionals underestimate De, with a magnitude that tends to increase with amount of FE and system size, averaging across structures these errors range from about −66 to −34%. The size-dependence of the error can be partially explained with the fact that dispersion effects are expected to increase with system size191 and that dispersion corrections have not been applied at this stage. Percentage errors in re are universally positive with magnitudes that decrease with percentage of FE, with errors averaged across structures ranging from 4 to 13%. Overall, with an increase in FE, errors in De and re increase and decrease, respectively. Despite the overall poor performance from global hybrids regardless of FE percentage we can still gain an insight into the impact FE has for the complicated effects of excimer binding.As De) with BLYP unable to bind the anthracene and pyrene excimers. As GGAs are well-known to produce large errors for excited states and offer no exception here, they are not explored in the subsequent benchmarking study.Without FE, generalised-gradient approximation (GGA) errors are larger than those of global hybrids  give the largest absolute errors of the global hybrids. An increase in De error with FE is somewhat surprising given that global hybrids with large amounts of FE generally describe CT and other long-range excitation effects better than smaller amounts of FE.60 High percentages of FE do improve the description of re which may reflect the improvement of these long-range excitation effects. However this improved description of re cannot overcome the poor description of De by these functionals and an overall error that increases with system size. Due to the opposing effects of FE on the recovery of both minimum characteristics, the most balanced functionals are those with 37.5% FE.Functionals with large amounts of FE tend to worsen the description of excimer binding across the four tested systems. Functionals with 20% FE yield the smallest absolute errors in De ranging between −56.6 and 7.3% while B3LYP errors range between −68.2 and −21.7%. This difference in behaviours is also exhibited by GGAs, where PBE binds all four excimers whereas BLYP is unable to bind the anthracene and pyrene excimers. Interaction energy curves of CCS, which can be thought of as the HF equivalent for electronic excited states, were plotted to offer a comparison to a method with no electron-correlation but 100% FE  and pyrene  excimers indicating that electron correlation plays a significant role in the stabilisation of those systems. PBE-based functionals can be thought to better describe the electron correlation contributions to the excimer states than BLYP based functionals. The difference between the two underlying XC functionals for the excimer state therefore parallels that of ground states, where PBE is more attractive than BLYP in the treatment of NCIs.42,84,192The PBE-based functionals yield larger dissociation energies than BLYP-based functionals which, as most of the functionals underestimate the excimer stability, more closely resemble the reference well; for example, PBE20 yields errors in re with error trends that increase with FE and system size, indicating the requirement of more sophisticated functionals for an accurate description of excimer binding. With increasing FE, errors in De increase while errors in re decrease such that the ability of a global hybrid TD-DFA to describe each quantity seems to require a trade-off in accuracy to the other. As both De and re must be correctly described in order to predict excimer binding, global-hybrid TD-DFAs do not offer reliable results. Methods from the higher rungs of Jacob's Ladder and additive dispersion corrections have been effective in addressing some of short-comings associated with global hybrids for ground states, so their performance will be addressed in the following sections.Despite the generally improved performance of PBE-based functionals, DFAs based on both XC expressions greatly underestimate the dissociation energy and overestimate 4.2i.e. De and re, are listed in In this section, the interaction energy curves for each excimer across a range of TD-DFAs are analysed relative to the reference of SCS-CC2/CBS. The chosen range of TD-DFAs is based on either popularity, established accuracy for single-molecule excitations, or novelty; they are: B3LYP, PBE38, BHLYP , CAM-B3LYP, ωB97X (RS hybrids), B2PLYP, B2GP-PLYP , ωB2PLYP and ωB2GP-PLYP (RS-DHDFAs). These functionals occupy the top two rungs of Jacob's Ladder with varying exchange-correlation components and FE percentages, with and without RS, as detailed in 4.2.1−1 at 2.97 Å (re). The ability to describe the shape and depth of the potential energy well differs from DFA to DFA. The assessed global hybrids  and overestimating re by 0.06–0.20 Å (2–7% error), some of the largest errors for this system. PBE38 is somewhat of an exception to the other global hybrids with a well-depth  and position (3.03 Å) in line with higher-rung double hybrids. However, as discussed in the FE study, global hybrids are not capable of reliably capturing the challenging interactions in excimer binding. Poor performance of global hybrids is consistent with their inability to accurately describe the CT, exciton coupling and dispersion interactions inherent to excimer binding.8,42,79,193 As we will see in the following sections, the performance of PBE38 is not as favourable for the larger systems tested.For the benzene excimer, excited-state interaction energies calculated across varied inter-monomer distances at the SCS-CC2/CBS level of theory  yield a re compared to its uncorrected counterpart B3LYP with an improvement from a deviation of 0.18 to 0.12 Å . Double hybrids yield an improved description of interaction energies along the dissociation curve, with B2GP-PLYP being closer to the reference than B2PLYP .The long-range correction in CAM-B3LYP reduces the overestimation in 47,66,77 Improved performance by DHDFAs additionally parallels the finding that only double hybrids were able to properly describe an exciton-coupled ECD spectrum,79 for which WFT methods had to be applied earlier.194 However, as recently re-emphasised, global double hybrids still fail to correctly describe CT excitations.63 The combination of range-separation and perturbative correction improves the description of the benzene excimer dissociation energy curve, giving the curves closest to the reference at all intermolecular distances  and the latter slightly overestimating it by 0.25 kcal mol−1 (2% error). Close comparison of RS-DHDFAs with the reference interaction energy curves of the benzene excimer display potential to corroborate claims of their robustness for local-valence and long-range excitations.52,53,62,64 In summary, it is observed that, for the benzene excimer, the description of binding is improved by climbing Jacob's Ladder with rung-five functionals showing considerable improvement over those belonging to rung four  dissociation energy of 28.32 kcal molt 3.04 Å . When asDe ranging between 3.65 and 16.53 kcal mol−1 (13–58% error). re is largely overestimated with absolute deviations ranging from 0.03 to 0.33 Å (0.3–11% error). The fourth-rung functionals behave differently between naphthalene and benzene excimers whereas fifth-rung functionals exhibit similar performance trends. For the naphthalene excimer PBE38 offers an re closer to the reference  than the BLYP based functionals, however underestimation of De is on par with other DFAs belonging to this rung (40% error), consistent with results from our previous FE study in Section 4.1. B3LYP binds the excimer with a De comparable to those of other global hybrids (48% error) while its long-range corrected counterpart, CAM-B3LYP, again improves the description of re (reduced deviation from 0.33 to 0.20 Å) but yields De akin to the global hybrids (53% error). While the relative trends between rung-four functionals differ between benzene and naphthalene excimers, the finding remains that global hybrids provide the worst results.The chosen exchange-correlation functionals uniformly predict a weaker binding with absolute errors of De and re, respectively. Further improvement on conventional DHDFAs results from the inclusion of range-separation with absolute errors in the order of 13–20% and 1–2% for De and re, respectively. Despite the closer resemblance of RS-DHDFAs curves with the reference curve .The anthracene excimer is slightly more stable than the naphthalene excimer, with an SCS-CC2/CBS dissociation energy of 28.40 kcal molf 3.18 Å . The herDe of the anthracene excimer being larger than that of the naphthalene excimer may be due to a larger dispersion contribution to the excimer binding.7 Given that the TD-DFT methods discussed in this sections are unable to describe dispersion, this further supports the study of dispersion-corrected functionals for excimer binding in Section 4.3.It was previously noted that the 4.2.4−1 at 3.19 Å. Similarly to the naphthalene dimer, we also observed the wrong order of states at the dissociation limit for some functionals, something that can be avoided when using symmetry in the calculation.The pyrene excimer  is more −1) which, relative to the difference between the reference De values , yields remarkably similar errors (21–75%). The trends observed for the naphthalene and anthracene excimers hold true for the pyrene excimer, with an improved description of excimer stabilisation moving up Jacob's Ladder.Each functional predicts similar dissociation energies as for the anthracene case .The analysis of De and re, with a slight improvement in re through range-separation; double hybrids improve upon the description of both well characteristics while range-separated double hybrids show the best description of both characteristics across the tested functionals. We saw an increase in the error of De with system size which may be due to the lack of properly treating dispersion interactions. In the following section we explore the application of ground-state optimised dispersion corrections to assess their potential in accounting for the missing dispersion in excimer binding.To summarise Section 4.2, the relative performance of the tested functionals follows a general trend: global hybrids and CAM-B3LYP perform the worst in terms of 4.38 In our introduction we have pointed out how some studies make use of dispersion-uncorrected methods for the treatment of excimers, but our results clearly show that dispersion effects should not be neglected. Herein, we demonstrate the impact of ground-state dispersion corrections for the two extreme cases in our study, namely the benzene dimer as the smallest and the pyrene dimer as the largest system.So far we have only discussed dispersion-uncorrected results. As dispersion-uncorrected TD-DFAs are able to partially predict excimer binding it is clear that interactions beyond dispersion are important, which aligns with the findings from an energy decomposition analysis reported in 2018.5,114,115 However, it is reasonable to expect dispersion interactions to change upon electronic excitation113 rendering any benefit application-dependent. Herein, we test these justifications for two schemes of additive DFT-D type dispersion corrections as applied to the excimer state without any state-specific adjustment. The DFT-D3(BJ) and DFT-D4—hereafter dubbed “D3(BJ)” and “D4”—dispersion energies were calculated for all points along the dissociation curves and added to the respective total excited-state energies. The analysis of these dispersion-corrected dissociation energy curves focuses on four functionals B3LYP, CAM-B3LYP and B2PLYP and ωB2PLYP, i.e. two global functionals and their range-separated counterparts . The corrections offer an improved but overestimated description of the optimal inter-monomer separation for B3LYP, CAM-B3LYP, and B2PLYP with errors between 0.03 and 0.07 Å for D3(BJ) and between 0.04 and 0.06 Å for D4. However, the improvement to re is drastically over-shadowed by the greatly overstabilised dissociation energy. Dispersion-corrected and -uncorrected ωB2PLYP give the same overestimation of re by 0.02 Å. As the smallest of the model systems, benzene excimer binding contains a smaller dispersion contribution than the larger models. With less dispersion to account for, more complex functionals are able to reasonably account for the other contributions to the dissociation energy without dispersion correction. The ground-state optimised corrections, thus, have a tendency to overestimate the dispersion contribution to the benzene excimer dissociation energy.For the benzene excimer, both dispersion corrections overcorrect the binding predicted by each TD-DFA except ωB2PLYP . WhetherDe in the range of 10.18–23.58 kcal mol−1  for all functionals, so as with benzene, the preference of D3(BJ) or D4 depends on whether the dispersion-corrected TD-DFA over or underbinds the pyrene excimer.The pyrene excimer is larger and more strongly bound than the benzene excimer, which the selected uncorrected TD-DFAs fail to predict, underestimating al mol−1 . For thi−1 accompanied by an improved re with an overestimation of 0.12 Å. Dispersion-corrected CAM-B3LYP does not show the same improvement to the dissociation energy as its global counterpart, yielding an underestimation of up to 5.90 kcal mol−1 for De and an overestimation of re by 0.14 and 0.13 Å for D3(BJ) and D4, respectively. B2PLYP-D3(BJ) and -D4 give dissociation energies with errors comparable to dispersion-corrected B3LYP , but with a smaller geometry error (overestimation of 0.07 and 0.08 Å). Dispersion corrected ωB2PLYP offers only a small improvement to the uncorrected functional such that ωB2PLYP-D3(BJ) and ωB2PLYP-D4 underbind the pyrene excimer by 9.66 and 9.63 kcal mol−1, respectively, and overestimate re by 0.08 Å. A negligible impact of D3(BJ) and D4 on both ωB2PLYP and ωB2GP-PLYP has also been noticed in ground-state benchmarking on the complete GMTKN55  correction reduces the repulsion yielding maxima of up to 0.02 kcal mol−1, which brings the two functionals into close comparison with each other . The D4 curves are also comparable in this region, although they exhibit larger maxima than D3(BJ) curves: 0.07 and 0.06 kcal mol−1 for B3LYP-D4 and B2PLYP-D4, respectively. The positive behaviour that remains after the applied corrections would not be expected with corrections appropriately parametrised for excited states. Interestingly, in a recent study of exciplex interaction energy curves, a similar unphysical repulsive hump exhibited by ωB97 also saw correction by ωB97X-D3 ] mostly corrects the unphysical repulsion of SCS-CC2/def2-TZVP, reducing the repulsion to less than 0.01 kcal mol-D3 ref.  with DFTWith this closer look at ground-state dispersion corrections for the binding of benzene and pyrene excimers, it is clear that accounting for dispersion is important for accurate calculation of dissociation curves in both the binding region and beyond. While ground-state optimised dispersion corrections offer some improvement to excimer binding, a state-specific reparametrisation for excited states would be necessary for robust and reliable TD-DFA results. An overarching discussion of the performance of dispersion corrections for all benchmarked DFAs is presented in the following section.4.4193 Here, the MAD for each characteristic averaged for each method is calculated by following the general form:i and REFERENCEi are the values of the property for the ith excimer, either De or re, and N the number of systems. An analysis of MADs is simply presented as a convenient metric to summarise the performance of a method across our four model structures, and we acknowledge a sample size of four does not offer MADs with statistical significance comparable to more comprehensive excited-state benchmarks.51,55,57,59,163–165,197 MADs for the nine functionals, with and without D3(BJ) and D4 dispersion corrections, compared to the SCS-CC2/CBS reference are presented in †Following our previous analysis of the interaction energy curves, we continue with an overall discussion of each functional's performance averaged across all systems both with and without dispersion corrections. Functional performance is almost universally assessed by mean absolute deviations (MADs) as the metric for benchmarking of quantum-chemical methods.De and re, dispersion-uncorrected functionals display a descending trend for the MADs while ascending Jacob's Ladder . This increase in deviation supports the tendency of global hybrids with large amounts of FE to cause issues for describing excitations in TD-DFT.67–70 For example, global hybrids with large components of FE tend to produce blue-shifted excitation energies in single molecules.55,57,66 Despite the established better description of CT excitations with range-separated hybrids, CAM-B3LYP performs worse than B3LYP. On the other hand, ωB97X, despite the aforementioned problems with obtaining smooth dissociation curves, proves to be the best tested dispersion-uncorrected hybrid in this study with MADs of 9.69 kcal mol−1 and 0.17 Å.For global hybrids, an increase in FE is generally associated with an increase in MAD for a and Lb according to Platt201—are poorly described by many TD-DFT methods, including global hybrids.195,202 RS hybrids can improve the description of La but blueshift Lb excitations.76,203 Double hybrids, particularly the latest range-separated ones, have to date yielded the most accurate and balanced description of both states in PAHs.52,53,58 This, in addition to the aforementioned better description of exciton coupling,79 most likely explains why DHDFAs are the best-performing methods in our study. The global DHDFAs B2PLYP and B2GP-PLYP have MADs of 8.50 and 6.47 kcal mol−1 for De and of 0.15 Å and 0.11 Å in re. The two dispersion-uncorrected RS-DHDFAs show even better MADs, most likely due to the better description of CT effects, but their MADs in De are still well above the accepted chemical-accuracy threshold of 0.1 kcal mol−1 for NCIs with values of 6.16 and 4.15 kcal mol−1 for ωB2PLYP and ωB2GP-PLYP. Their values for re are 0.05 and 0.04 Å, respectively.We have already mentioned problems in state order for the naphthalene and pyrene dimers in Sections 4.2.2 and 4.2.4, but still need to elaborate more in detail on the fact that the dimers consist of polycyclic aromatic hydrocarbons (PAHs). Single-molecule studies of PAHs have established that the first two π–π* excitations in PAHs—called LIn conclusion, all tested dispersion-uncorrected functionals fail to recover excimer binding of SCS-CC2/CBS quality.De than for re. However, the improvement to excimer binding by the tested dispersion corrections shown through this reduction in MADs is not predictable. While dispersion-uncorrected functionals yield errors due to underestimation of De and overestimation of re, dispersion corrections under or overcorrect depending on the system and functional. D4 and D3(BJ) yield similar De MADs in the order of 0.96–5.82 kcal mol−1 and 0.80–5.83 kcal mol−1, respectively. For the same underlying functional, the two iterations of DFT-D yield comparable MADs where differences between D4 and D3(BJ) MADs do not exceed 0.02 Å or 1.16 kcal mol−1.The application of D3(BJ) and D4 dispersion corrections shows significantly reduced MADs across all tested functionals, excluding ωB2(GP-)PLYP, with larger reductions observed for re (ranging from 0.05 to 0.07 Å) and the smallest deviations in De despite their tendency to overbind the excimer systems: their MADs for De range from 0.80 kcal mol−1 [B2GP-PLYP-D3(BJ)] to 1.85 kcal mol−1 [B2PLYP-D4]. Overestimation of exciplex binding from dispersion-corrected double hybrids was also noted in the study by Krueger and Blanquart where B2PLYP-D3(BJ) significantly overbound the exciplexes analysed which the authors acknowledged was largely due to the inclusion of a dispersion correction.102 Their tendency to overestimate De suggests that excited-state parametrised dispersion corrections would be necessary for a reliable description by TD-DFT methods.Dispersion-corrected global double hybrids give the best description of excimer binding with greatly improved De that range from 4.14 [ωB2GP-PLYP-D3(BJ)/D4] to 5.83 kcal mol−1 [ωB2PLYP-D3(BJ)]. MADs in re are unchanged from dispersion-uncorrected RS-DHFAs (0.04–0.05 Å) remaining the best performing across all functionals dispersion-corrected or otherwise. As the first application of ground-state parametrised dispersion corrections to RS-DHDFAs for excited-state problems, these functionals display potential for TD-DFT dissociation energies that approach SCS-CC2/CBS quality. However, their tendency to underestimate De reinforces the necessity of excited-state parametrised dispersion corrections for a reliable description by TD-DFT methods.Dispersion-corrected RS-DHDFAs only slightly improve on dispersion-uncorrected results, with MADs for From the discussion of dispersion-uncorrected functionals, double hybrids and range-separated double hybrids performed well for the more complicated excited-state interactions comprising excimer binding. As with range-separated double hybrids, the ground-state parametrised dispersion corrections do not reliably account for excited-state dispersion interactions, but without accounting for this missing dispersion TD-DFT cannot provide reliable results for excited states. While with current dispersion corrections both types of DHDFAs seem to be adequate, it is safe to assume that the better description of CT with RS-DHDFAs means that they will prevail once paired with state-specific corrections.De in the order of 2.15–4.36 kcal mol−1, more comparable to the MADs of higher-rung dispersion-corrected functionals, alongside an improved but still overestimated re with MADs ranging from 0.07 to 0.12 Å. The dispersion corrections offer considerable improvement to excimer binding for these less sophisticated functionals which gave the largest MADs when dispersion-uncorrected. However, even with dispersion correction, global hybrids and CAM-B3LYP are still consistently outperformed by DHDFAs.Global hybrids and CAM-B3LYP show a significant error reduction upon dispersion correction yielding MADs for 5De and inter-monomer equilibrium distances re.The binding of four different aromatic excimer models was analysed by means of dissociation curves. To our knowledge, this is the first study to provide single-reference wave function curves at the complete basis set (CBS) limit for aromatic excimer systems. More specifically, linear SCS-CC2/CBS was established as a reliable reference that allowed us to shed light onto various TD-DFT methods including a detailed analysis of excimers with double-hybrid density functionals and the first application of range-separated double hybrids to such systems. Our main goal was to address the impact of Fock exchange, range separation, the perturbative nonlocal correction used in double hybrids, and London dispersion corrections. We analysed two quantities that characterise the minima along the dissociation curves, namely dissociation energies De and re with hybrid functionals, whereas double hybrids provided a more robust picture. We found no ideal admixture of Fock exchange in global hybrids as its increase led to smaller dissociation energies and larger equilibrium distances, with large errors across both quantities. Dispersion-uncorrected global and range-separated hybrids, as well as global and range-separated double hybrids, all gave curves with distinct minima, with the latter functional type giving the best curves, most likely due to a better description of charge-transfer and exciton coupling. That being said, all dispersion-uncorrected TD-DFT methods produced large errors that increased considerably with system size. For the smallest system, the benzene excimer, dispersion-uncorrected methods see the best results from range-separated double hybrids, approaching the accuracy of SCS-CC2/CBS quality. However, for larger systems there was greater disparity between even the most accurate TD-DFT methods and the reference. De values were usually underestimated and re values overestimated, which points to missing dispersion interactions as the likely reason.Overall, it turned out to be challenging to obtain a good description of both The application of ground-state parametrised dispersion corrections generally reduced the errors of dispersion-uncorrected functionals but did not reach chemical accuracy most likely due to not having been designed to describe excited states. We have noticed overstabilisation of some systems for some functionals, which occurred more often for the smaller systems. For some methods and systems, improvements of the minimum-energy regions were observed, but dissociation energies were still underestimated. To our knowledge, we were also the first to point out that most TD-DFT methods were unphysically repulsive in the mid range, something that could be reduced by applying dispersion corrections, which in turn indicated that dispersion was the most dominant contribution in that range.52,53,62–64,66 However, we have also shown that there is a need for the development of state-specific London dispersion corrections to achieve a reliable and robust TD-DFT description of excimers and related systems for all tested methods, including range-separated double hybrids.Our study has shown that some of the latest and most modern TD-DFT methods, namely range-separated double hybrids, belong to the most robust and accurate when treating excited states, which parallels single-molecule studies.There are no conflicts of interest to declare.RA-013-D3RA07381E-s001RA-013-D3RA07381E-s002